A246366 Permutation of natural numbers: a(n) = A005941(A227413(n)).

1, 2, 4, 3, 6, 9, 7, 5, 8, 33, 12, 65, 18, 257, 16, 17, 10, 129, 11, 4097, 34, 2049, 19, 65537, 15, 8193, 24, 4194305, 21, 32769, 66, 1025, 20, 513, 14, 262145, 22, 16385, 13, 1099511627777, 1026, 2097153, 130, 68719476737, 30, 1048577, 35, 288230376151711745, 8194, 67108865, 40, 4398046511105, 2050, 8388609, 28

Offset: 1

Author

Antti Karttunen, Aug 26 2014

Keywords

• nonn

Comments

Maps even numbers to terms of A000051 (2^n + 1) in some order.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..95
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Inverse: A246365.

Related or similar permutations: A005941, A156552, A227413, A246364, A246368.

Cf. A000051.

Programs

PARI

default(primelimit,(2^31)+(2^30));
A002808(n) = { my(k=-1); while( -n + n += -k + k=primepi(n), ); n }; \\ This function from M. F. Hasler
A064989(n) = {my(f); f = factor(n); if((n>1 && f[1,1]==2), f[1,2] = 0); for (i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f)};
A156552(n) = if(1==n, 0, if(!(n%2), 1+(2*A156552(n/2)), 2*A156552(A064989(n))));
A005941(n) = A156552(n)+1;
A227413(n) = if(1==n, 1, if(!(n%2), prime(A227413(n/2)), A002808(A227413((n-1)/2))));
A246366(n) = A005941(A227413(n));
for(n=1, 95, write("b246366.txt", n, " ", A246366(n)));

Scheme

(define (A246368 n) (A227413 (A005941 n)))

Formula

a(n) = A005941(A227413(n)) = 1 + A156552(A227413(n)).